Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 7, 2008, Pages 2158-2166

  Lee, Haewon ^a   Alkahby, Hadi ^a  

^a DILLARD UNIVERSITY   (United States)

Author keywords

Almost automorphic; Constant delay; Nonautonomous equations; Regular solutions

Indexed keywords

DIFFERENTIAL EQUATIONS; EVOLUTIONARY ALGORITHMS; LINEAR EQUATIONS; MATHEMATICAL MORPHOLOGY; SOLUTIONS;

EXISTENCE AND UNIQUENESS; NON AUTONOMOUS; SEMILINEAR EVOLUTION EQUATIONS;

NUMERICAL METHODS;

EID: 45349088776     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.07.053     Document Type: Article

References (15)

1. Acquistapace P., and Terreni B. A unified approach to abstract linear parabolic equations. Rend. Sem. Mat. Univ. Padova 78 (1987) 47-107
2. Bochner S. Uniform convergence of monotone sequences of functions. Proc. Natl. Acad. Sci. USA 47 (1961) 582-585
3. Bochner S. A new approach to almost periodicity. Proc. Natl. Acad. Sci. USA 48 (1962) 2039-2043
4. Bochner S. Continuous mappings of almost automorphic and almost periodic functions. Proc. Natl. Acad. Sci. USA 52 (1964) 907-910
5. N'Guérékata G.M., and Pankov A. Stepanov-like almost automorphic functions and monotone evolution equations. Nonlinear Anal. TMA (2007) 10.1016/j.na.2007.02.012
6. Diagana T., and N'Guérékata G.M. Stepanov-like almost automorphic functions and applications to some semilinear equations. Appl. Anal. 86 (2007) 723-733
7. N'Guérékata G.M. Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations. Semigroup Forum 69 (2004) 80-86
8. Bugajewski D., and Diagana T. Almost automorphy of the convolution operator and applications to differential and functional-differential equations. Nonlinear Stud. 13 (2006) 129-140
9. Veech W.A. Almost automorphic functions. Proc. Natl. Acad. Sci. USA 49 (1963) 462-464
10. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences vol. 44 (1983), Springer-Verlag, New York
11. Engel K.J., and Nagel R. One-Parameter Semigroups for Linear Evolution Equations (2000), Springer, New York
12. Andres A., Bersani A.M., and Grande R.F. Hierarchy of almost-periodic function spaces. Rend. Mat., Ser. VII 26 (2006) 121-188
13. Cooke R.L. Almost-periodic functions. Amer. Math. Monthly 88 (1981) 515-526
14. Ding H.S., Liang J., N'Guérékata G.M., and Xiao T.J. Pseudo-almost periodicity of some nonautonomous evolution equations with delay. Nonlinear Anal. TMA 67 (2007) 1412-1418
15. Ding H.S., Liang J., N'Guérékata G.M., and Xiao T.J. Mild pseudo-almost periodic solutions of nonautonomous semilinear evolution equations. Math. Comput. Modelling 45 (2007) 579-584